Abstract

In the coupled-dipole method an arbitrary particle is modeled as an array of N polarizable subunits, each of which gives rise to only electric dipole radiation. The Clausius-Mosotti relation is widely used to calculate the polarizability of the subunits that correspond to the dielectric function of the particle that the array represents. We replace the Clausius-Mosotti relation with an exact expression for the electric dipole polarizability and find improvement in extinction calculations for spheres as compared with Mie theory. Near a Fröhlich frequency the coupled-dipole method yields extinction cross sections for spheres and spheroids that compare favorably with the continuous distribution of ellipsoids method and measured values.

References

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Table 1

Comparison of Qext for Nine Spheres of Different Refractive Indices as Calculated by Mie Theory and by the Coupled-Dipole Method with the Doyle Expression, Draine’s Radiative-Reaction Term, or the CM Relationa

Refractive Index

Doyle

Draine

CM

ka|m|

1.44 + i0.26

−0.010

−0.010

−0.010

0.29

1.33 + i0.05

−0.017

−0.033

−0.050

0.34

1.55 + i0.005

−0.068

−0.111

−0.128

0.39

1.39 + 0.42

0.000

−0.011

−0.006

0.37

1.7 + i0.1

−0.071

−0.124

−0.128

0.42

1.9 + 0.0004

−0.103

−0.187

−0.184

0.48

2.5 + i1.4

0.141

0.160

0.167

0.72

3.5 + i2.05

0.173

0.197

0.153

1.02

3.0 + i4.0

0.300

0.181

0.369

1.26

a Values shown are [QextQext(Mie)-1]. A 136-dipole array is used for the coupled-dipole calculations; the effective radius of the sphere remains constant at 3.19 du. Rows are in order of increasing size parameter of the dipolar subunit.

Table 2

a All dipole arrays represent a spherical particle of radius 0.5 pm. Columns represent number of dipoles, radius of gyration, and maximum value of Cext/v near the 1153-cm−1 Fröhlich frequency as calculated by the coupled-dipole method. Rows are in order of decreasing sphericity as determined by Draine’s criterion. The corresponding Cext/v calculated by Mie theory is 17.1 μm−1.

Tables (2)

Table 1

Comparison of Qext for Nine Spheres of Different Refractive Indices as Calculated by Mie Theory and by the Coupled-Dipole Method with the Doyle Expression, Draine’s Radiative-Reaction Term, or the CM Relationa

Refractive Index

Doyle

Draine

CM

ka|m|

1.44 + i0.26

−0.010

−0.010

−0.010

0.29

1.33 + i0.05

−0.017

−0.033

−0.050

0.34

1.55 + i0.005

−0.068

−0.111

−0.128

0.39

1.39 + 0.42

0.000

−0.011

−0.006

0.37

1.7 + i0.1

−0.071

−0.124

−0.128

0.42

1.9 + 0.0004

−0.103

−0.187

−0.184

0.48

2.5 + i1.4

0.141

0.160

0.167

0.72

3.5 + i2.05

0.173

0.197

0.153

1.02

3.0 + i4.0

0.300

0.181

0.369

1.26

a Values shown are [QextQext(Mie)-1]. A 136-dipole array is used for the coupled-dipole calculations; the effective radius of the sphere remains constant at 3.19 du. Rows are in order of increasing size parameter of the dipolar subunit.

Table 2

a All dipole arrays represent a spherical particle of radius 0.5 pm. Columns represent number of dipoles, radius of gyration, and maximum value of Cext/v near the 1153-cm−1 Fröhlich frequency as calculated by the coupled-dipole method. Rows are in order of decreasing sphericity as determined by Draine’s criterion. The corresponding Cext/v calculated by Mie theory is 17.1 μm−1.